Figure 10-6. Specifications for determining the CG of an airplane using weight and arm.
Figure 10-7. Specifications for determining the CG of an airplane
using weights and moment indexes.
Weight Point Weight (lb) Arm (in) Moment (lb-in) CG
106,240
107,008
17,000
230,248 114.8
Right side
Left side
Nose
Total
830
836
340
2,006
128
128
50
Weighing Point Weight (lb) Moment/100 CG
114.8
Right side
Left side
Nose
Total
830
836
340
2,006
1,062.4
1,070.1
170
2,302.5
Determining CG, Given Weights, and Arms
Some weight and balance problems involve weights and arms
to determine the moments. Divide the total moment by the
total weight to determine the CG. Figure 10-6 contains the
specifications for determining the CG using weights and arms.
Determine the CG by using the data in Figure 10-6 and
following these steps:
1. Determine the total weight and record this number:
(830)(+)(836)(+)(340)(=) 2,006
2. Determine the moment of each weighing point and
record them:
(830)(×)(128)(=) 106,240
(836)(×)(128)(=) 107,008
(340)(×)(50)(=) 17,000
3. Determine the total moment and divide this by the
total weight:
(106240)(+)(107008)(+)(17000)(=)(÷)(2006)(=)
114.8
This airplane weighs 2,006 pounds and its CG is 114.8 inches
from the datum.
Determining CG, Given Weights, and Moment
Indexes
Other weight and balance problems involve weights and
moment indexes, such as moment/100 or moment/1,000. To
determine the CG, add all the weights and all the moment
indexes. Then, divide the total moment index by the total
weight and multiply the answer by the reduction factor.
Figure 10-7 contains the specifications for determining the
CG using weights and moments indexes.
Determine the CG by using the data in Figure 10-7 and
following these steps:
1. Determine the total weight and record this number:
(830)(+)(836)(+)(340)(=) 2,006
2. Determine the total moment index, divide this by the
total weight, and multiply it by the reduction factor
of 100:
(1062.4)(+)(1070.1)(+)(170)(=)(2302.5)(÷)(2006)(=)
(1.148)(×)(100)(=) 114.8
This airplane weighs 2,006 pounds and its CG is 114.8 inches
from the datum.
Determining CG in Percent Mean Aerodynamic
Chord (MAC)
• The loaded CG is 42.47 inches aft of the datum.
• MAC is 61.6 inches long.
• LEMAC is at station 20.1.
1. Determine the distance between the CG and LEMAC:
(42.47)(–)(20.1)(=) 22.37
2. Then, use this formula:
(22.37)(×)(100)(÷)(61.6)(=) 36.3
The CG of this airplane is located at 36.3 percent MAC.
Determining Lateral CG of a Helicopter
For a helicopter, it is often necessary to determine not only
the longitudinal CG, but the lateral CG as well. Lateral CG is
measured from butt line zero (BL 0). All items and moments
to the left of BL 0 are negative, and all those to the right of
BL 0 are positive. Figure 10-8 contains the specifications for
determining the lateral CG of a typical helicopter.
Figure 10-8. Specifications for determining the lateral CG of a helicopter.
Item Weight (lb) Lateral Arm (in) Lateral Offset Moment (lb-in) Lateral CG
309
−2,295
2,700
−2,419
−1,705 –0.77
Helicopter empty weight
Pilot
Passenger
Fuel (48 gal)
Total
1,545
170
200
288
2,203
+0.2
–13.5
+13.5
135.0
–8.4
x =
Determine the lateral CG by using the data in Figure 10-8 and
following these steps:
1. Add all of the weights:
(1545)(+)(170)(+)(200)(+)(288)(=) 2,203
2. Multiply the lateral arm (the distance between butt
line zero and the CG of each item) by its weight to
get the lateral offset moment of each item. Moments
to the right of BL 0 are positive and those to the left
are negative.
(1,545)(×)(.2)(=) 309
(170)(×)(13.5)(+/–)(=) –2,295
(200)(×)(13.5)(=) 2,700
(288)(×)(8.4)(+/–)(=) –2,419
3. Determine the algebraic sum of the lateral offset
moments.
(309)(+)(2295)(+/–)(+)(2700)(+)(2419)(+/–)(=)
–1,705
4. Divide the sum of the moments by the total weight to
determine the lateral CG.
(1705)(+/–)(÷)(2203)(=) –0.77
The lateral CG is 0.77 inch to the left of BL0.
Determining ΔCG Caused by Shifting Weights
Fifty pounds of baggage is shifted from the aft baggage
compartment at station 246 to the forward compartment at
station 118. The total airplane weight is 4,709 pounds. How
much does the CG shift?
1. Determine the number of inches the baggage is shifted:
(246)(–)(118)(=) 128
2. Use this formula:
Δ CG = Weight shifted × Distance weight is shifted
Total weight
(50)(×)(128)(÷)(4709)(=) 1.36
The CG is shifted forward 1.36 inches.
Determining Weight Shifted to Cause Specified
ΔCG
How much weight must be shifted from the aft baggage
compartment at station 246 to the forward compartment
at station 118 to move the CG forward 2 inches? The total
weight of the airplane is 4,709 pounds.
1. Determine the number of inches the baggage is shifted:
Weight shifted = Total weight shifted × Δ CG
Distance weight is shifted
(246)(–)(118)(=) 128
2. Use this formula:
(2)(×)(4709)(÷)(128)(=) 73.6
Moving 73.6 pounds of baggage from the aft compartment
to forward compartment shifts the CG forward 2 inches.
Determining Distance Weight Is Shifted to Move
CG a Specific Distanc
How many inches aft does a 56 pound battery need to be
moved to shift the CG aft by 1.5 inches? The total weight of
the airplane is 4,026 pounds.
Use this formula:
Distance weight is shifted = Total weight × Δ CG
Weight shifted
(1.5)(×)(4026)(÷)(56)(=) 107.8
Moving the battery aft by 107.8 inches shifts the CG aft 1.5
inches.
Determining Total Weight of an Aircraft With a
Specified ΔCG When Cargo Is Move
What is the total weight of an airplane if moving 500 pounds
of cargo 96 inches forward shifts the CG 2.0 inches?
Use this formula:
Total weight = Weight shifted × Distance weight is shifted
Δ CG
(500)(×)(96)(÷)(2)(=) 24,000
Moving 500 pounds of cargo 96 inches forward causes a
2.0-inch shift in CG of a 24,000-pound airplane.
Determining Amount of Ballast Needed to Move
CG to a Desired Location
How much ballast must be mounted at station 228 to move
the CG to its forward limit of +33? The airplane weighs
1,876 pounds and the CG is at +32.2, a distance of 0.8 inch
out of limit.
Use this formula:
Ballast weight = Aircraft empty weight × D i s t . o u t o f l i m i t s
Distance ballast to desired CG
(1876)(×)(.8)(÷)(195)(=) 7.7
Attaching 7.7 pounds of ballast to the bulkhead at station
228 moves the CG to +33.0.